Angela Throgmorton is leading a somewhat lonely life when a strange, scruffy, creature appears on her doorstep. Feeling sorry for the poor thing, she takes it in, feeds it and cleans it up. However, when the creature manages to flood the house, Angela decides to find another home for it. This soon teaches Angela two lessons: firstly, that no-one wants the creature; and, secondly, that she really quite likes him. However, Old Tom and Angela get separated, and Angela goes home alone. Then a storm hits. Angela, learning that the creature has taken shelter in a storm drain, goes off to rescue him. Surfing through the drain on her ironing board, Angela snatches her new friend just before the storm-waters can wash him away. Angela takes him home and calls him Old Tom.

Angela goes shopping for a playhouse for Old Tom and ends up buying an old rocket ship. Old Tom loves it and, with his best friend Lucy, they decide to fly it to Mars. Angela thinks they are just playing (after all, the booster rockets have been taken off) and she goes along with their little 'fantasy'. However, while she is cleaning the rocket, it takes off - Old Tom had used one of Angela's vacuum cleaners as the propulsion. The rocket flies off into space with Old Tom on the inside, and Angela on the outside, battling meteors and satellites. Finally, Old Tom lets her in, just as the rocket careens out of control and crash lands on an unknown planet. Angela is sure they're on Mars - but one of the aliens looks familiar. It's Lavinia, and they have literally 'crashed' her garden party.

Old Tom is upset when Lucy has to go to a friend's party, so Angela takes him to the beach to cheer him up. As Angela dozes, Old Tom gets up to mischief. He grabs hold of the tail of a kite, which carries him out over the sea and drops him onto what looks like a pirate ship. However, it turns out to be a pirate-themed children's party, and Old Tom eats all the food. When the kids discover what he has done, they tie him up and threaten him with 'Scarface, the meanest pirate of them all'. However 'Scarface' is really Lucy, and Old Tom is untied. Before the party can resume, the birthday boy's father, who has fallen overboard, is chased by a shark, so Old Tom grabs a rope and rescues him.

The Queen, wanting to see someone different at her next garden party, choses Angela and Old Tom at random. Angela is delighted, but gives Old Tom a crash course in manners, just in case. The garden party begins, but the Queen doesn't want to go, because her dog doesn't seem well. Meanwhile, Old Tom upsets several party guests and seeks refuge from them in the palace. There he annoys the Queen's dog, which chases him around the throne room. The Queen enters and, delighted to see her dog full of life again, decides to go to the garden party after all - with Old Tom as her guest of honor.